So it is logical that she has thrown herself into the fight for a higher minimum wage in the state, a movement that has quickly gained traction. The state Senate passed a hike in the wage Tuesday, voting to raise the minimum to $11 by 2016; House action will follow. Separately, an initiative petition would place the issue of minimum wage before voters next year.

Conway helped collect signatures to place the petition on the ballot.

“People have said that this is an issue that matters, and one that can’t wait any longer,” Conway said Tuesday. “People are choosing between heat and food.”

While the bill winding its way through the State House differs from the petition in certain details, the goals are the same. Both would substantially raise the minimum wage. They would also increase the minimum wage for workers who receive tips; their hourly pay is lower because of the tip income. And both the legislation and the petition initiative would tie the minimum wage to inflation, eliminating the need for tough political fights every few years.

Organizers for the advocacy group Raise Up Massachusetts have collected 275,000 signatures for its ballot initiative. The movement has been mostly fueled by organized labor. The efforts seem to have struck a chord with people who are concerned about low-wage workers who are just scraping by financially.

“I really feel that the public sees this as a problem,” said Susan Tousignant, president of SEIU Local 509. “So many people are suffering because of low wages. Their families are affected, their children are affected.”

Senate passage of an increase was virtually guaranteed when President Therese Murray gave the bill her blessing, and passage in the House looks likely — though not certain. Tousignant is guardedly optimistic about the bill’s approval by the House.

“There’s no guarantee that this is going to pass,” she said. “But we believe the public is behind us.”

One late change in the legislation was the move to raise the minimum for workers who rely on tips. In theory, employees are supposed to offset any gap between their actual earnings and the minimum wage, but that doesn’t always happen. To call enforcement lax would be an understatement.

“Relying on tips is an unstable way of maintaining your income,” Conway said. “As schedules change and shifts change from week to week, you make substantially different amounts.”

In various guises, economic issues have demonstrated broad appeal lately. Marty Walsh’s election as Boston mayor was largely fueled by organized labor and by his pledges to stand with “working families.” Poverty is now taken seriously as a political issue. So is affordable housing, which has long been the subject of lip service, and little else. Raising the minimum wage is part of a much larger goal.

Conway, who’s 23, said she turned to working in a restaurant after realizing she was not drawn to the office jobs she had been working in. While she welcomes working in a food-related field, something she has a real passion for, she was shocked to discover it does not offer the benefits she has taken for granted, like paid sick time.

“It’s a big culture shock coming from a salaried job where I had all these benefits to having Mass Health,” she said.

The bid to raise the living standard of low-wage workers is still in its early stages, supporters caution. “It’s really only a start,” said SEIU’s Tousignant. “It’s still very expensive to live in Massachusetts.”